### Abstract

Suppose that G is a second countable, locally compact Hausdorff groupoid with abelian stabiliser subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid C* -algebra to have Hausdorff spectrum. In particular, we show that the spectrum of C*(G) is Hausdorff if and only if the stabilisers vary continuously with respect to the Fell topology, the orbit space {G}^{(0)} G is Hausdorff, and, given convergent sequences χ_{i} → χ and γ_{i} ̇ χ_{i} →ω in the dual stabiliser groupoid S where the γ_{i} G act via conjugation, if χ and ω are elements of the same fibre then χ = ω.

Original language | English (US) |
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Pages (from-to) | 232-242 |

Number of pages | 11 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 88 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1 2013 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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*Bulletin of the Australian Mathematical Society*, vol. 88, no. 2, pp. 232-242. https://doi.org/10.1017/S0004972713000129

**Groupoid C*-Algebras with Hausdorff spectrum.** / Goehle, Geoff.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Groupoid C*-Algebras with Hausdorff spectrum

AU - Goehle, Geoff

PY - 2013/10/1

Y1 - 2013/10/1

N2 - Suppose that G is a second countable, locally compact Hausdorff groupoid with abelian stabiliser subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid C* -algebra to have Hausdorff spectrum. In particular, we show that the spectrum of C*(G) is Hausdorff if and only if the stabilisers vary continuously with respect to the Fell topology, the orbit space {G}(0) G is Hausdorff, and, given convergent sequences χi → χ and γi ̇ χi →ω in the dual stabiliser groupoid S where the γi G act via conjugation, if χ and ω are elements of the same fibre then χ = ω.

AB - Suppose that G is a second countable, locally compact Hausdorff groupoid with abelian stabiliser subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid C* -algebra to have Hausdorff spectrum. In particular, we show that the spectrum of C*(G) is Hausdorff if and only if the stabilisers vary continuously with respect to the Fell topology, the orbit space {G}(0) G is Hausdorff, and, given convergent sequences χi → χ and γi ̇ χi →ω in the dual stabiliser groupoid S where the γi G act via conjugation, if χ and ω are elements of the same fibre then χ = ω.

UR - http://www.scopus.com/inward/record.url?scp=84883639821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883639821&partnerID=8YFLogxK

U2 - 10.1017/S0004972713000129

DO - 10.1017/S0004972713000129

M3 - Article

AN - SCOPUS:84883639821

VL - 88

SP - 232

EP - 242

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 2

ER -